2015 AP Physics 1 free response 2 c and d

Let's now tackle the rest of this problem. They say a light bulb is nonic if its resistance changes as a function of current. Your setup from part A, which we have right over here, is to be used or modified to determine whether the light bulb is nonic.

How, if at all, does the setup need to be modified? Well, we want to be able to change the current that's going through the light bulb and then see how the resistance changes. So what we could do, we can always measure with the setup right over here. It's very easy to measure the resistance.

We can measure resistance by knowing that V is equal to... we know that voltage is equal to current times resistance or that resistance is equal to voltage divided by current. So if we know the current going through a light bulb and we know the voltage across it, we can always figure out the resistance of the light bulb.

So our setup right here is actually very good for figuring out the resistance of the actual light bulb. We need to change the current and see how the resistance changes. There are a couple of ways that we could change the current. We could change some other resistance here, but lucky for us, we have a variable power source, so we can change the voltage.

We could change the voltage across the entire circuit. By changing the voltage across the entire circuit, well, that's going to change the current that is going through this simple circuit. It’s just going in series; the current is just doing like that.

So if we change the current through the entire circuit, we would be changing the current through the light bulb, and then we can just measure V and I and figure out whether R changes as well. So how, if at all, does the setup need to be modified? I could say it doesn't need to be modified; it doesn't need modification.

All right, and then the next section, what additional data, if any, would need to be collected? Well, I would want to measure… let me write this part down. Let me do it Part C over here. So part one of part C was no modification, no modification.

Nevermind, I can explain that. I can change resistance or I can change; I can change to current by varying the power source. By varying the power source, I can measure the resistance of the bulb by the voltage across the bulb divided by the current entering or exiting the bulb.

In the first part of this test, we were saying, “Hey, do we have the same number of electrons per second entering the bulb or exiting the bulb?” But from what we know of currents, we know that the current is going to be the same on either side. You have a voltage drop, but the current is the same.

So entering or exiting, you're going to get the same value. And even if you didn't know what I just told you, the first part of the experiment would have told you that your current is the same entering and exiting the bulb.

So this right over here is going to be equal to the resistance of the bulb. I can change the current by varying the power source, and then I can see what value I get for R by measuring these things as I change that overall current for my setup.

Let’s see part B: What additional data, if any, would need to be collected? So part two, part two here, I need to collect the voltage across the bulb as current changes or maybe as I change my variable power source.

As I vary the power source, I would also have to collect… maybe I'll write this way: I’ll collect that voltage. All right, like that: voltage across the bulb as I vary the power source, and I could say current entering or exiting the bulb as I vary the power source.

I have to measure these things, and then I'll be able to figure out if my R changes. All right, let's tackle Part D now. How would you analyze the data to determine whether the bulb is nonic? Include a discussion of how the uncertainties in the voltmeters and ammeters would affect your argument for concluding whether the resistance is nonic.

Well, I explained it a little bit, uh, well, up here, but I'll write it again. So let me read that one more time: How would you analyze the data? What I would do is vary the power source. I would make one voltage, measure what is described above, and use it to calculate the resistance of the bulb.

Then I'd vary the power source to a second voltage and once again measure above, to see if resistance changes.

So we could say if V across the bulb over… let me actually write it this way; all the V's are across the bulb. If V1 over I1, the voltage across the bulb over the current across the bulb, is equal to after I change it, I the voltage across the bulb divided by the current across the bulb.

If this over here, if these are equal, then I am dealing with the resistance that has not changed. So we could say, well, nonic is when the resistance does change. If resistance…

So we could say non-nomic. I could say not nonic. Otherwise, if V1 over I1 does not equal V2 over I2, then we are non-omic. And we have to be careful because the sensitivities of our voltmeters and ammeters might give us an aberrant result.

For example, we might be non-omic, but because of how we're rounding in the measurement, it actually might give us a change, especially because our ammeter is more sensitive.

On the other hand, we might be in a situation where we are nonic, but it doesn't register the change because it hasn't been large enough to be registered by the sensitivity of your instruments.

So we need to be careful about instrument sensitivity. The rounding to the nearest 0.1 Volt or 0.01 Amp could result in a difference in V over I when there isn't any, or vice versa.

It might not result in a difference, but there actually might be a change, but it's not big enough to be measured or vice versa. So you always have to be careful when you're doing any experiment in any science about how sensitive your actual instruments are and what the rounding might do for these calculations.